Question

heelp for the surface with parametric equations r(s,t)=, find the equation of the tangent plane at (2,3,1) Also Find the surface area under the restriction s^2+t^2<=1.

Answer 1

heelp for the surface with parametric equations r(s,t)=<st, s+t, s-t>, find the equation of the tangent plane at (2,3,1) Also Find the surface area under the restriction s^2+t^2<=1.

Answer 2

do you know how to find the normal vector of a parametric surface?

Answer 3

Do you know how to find a plane given a normal vector and a point?

Answer 4

no i only know if its in x y z

Answer 5

Give me a second... brb

Answer 6

Okay, the normal vector to the parametric surface \(\mathbf{r}(s,t)\)
Is given by \[\large
\mathbf{r}_s\times \mathbf{r}_t
\]That is, the cross product each of its partial derivatives.

Answer 7

@dan815 Think you can do that part at least?

Answer 8

You will get the normal vector as a function of \(s,t\)

Answer 9

Since the normal vector is changing

Answer 10

-2, t+s, t-s

Answer 11

wut do i do after i get the nomal vector

Answer 12

Find \(s,t\) such that \(\mathbf{r}(s,t)=(2,3,1) \)

Answer 13

Then plug in that \(s,t\) to find the normal vector to the point \((2,3,1) \)

Answer 14

ohh ok thanks i get it now

Answer 15

-2x+3y-z=4